PPC for generating leads - how does customer reacting being redirected?

I want to set up a PPC campaign for generating leads (in the auto/insurance/finance space).

I'm curious as to how conversion would be affected if a customer went to my domain (say for example getcheapinsurance.com), then to my landing page and THEN to the customers landing page where I get paid for the lead they fill out.

Would customers find it weird that they clicked to go to my site (getcheapinsurance.com) and then redirected to the advertisers landing page?

Well, how would YOU feel? I think you sort of answered your own question.

First, your domain's home page is a landing page. If you provide the information they asked for in their search, no reason to go to another page on your site. Typically, that's not the case and your ad will take them directly to the appropriate page. So if they searched for auto insurance, you take that click to a page about auto insurance. If home insurance, that click should land on a page about home insurance.

What I gather you are doing is trying to get your visitors to click through to an affiliate. If you send them to the affiliate's sales page, that's against most PPC services TOS, including Google Adwords and Bing. It's called a bridge page.

Think about it and put yourself in your prospect's shoes. You do a search and click an ad (or even an organic listing) and land on a page that is what you're looking for. You're sold and ready to buy so you click the "buy" button only to be shown another sales page. It's like being in a store where a clerk makes their sales pitch and when you say you'll take it, another clerk comes to do their sales pitch. So yeah, that's weird. Just take them to the checkout when they say they are ready to buy. Nobody wants to hear two sales pitches. Make it so that it's quick and easy to buy, the least number of clicks, the most direct path.

Ultimately the data is collected through their landing page and given I can't direct link, my page would have to act as some sort of feeder page to the advertisers landing page, in order to collect the data.

UNLESS, I work with the advertiser directly and capture the data myself and send it over via API...

But I know most people don't do that so how do they get away with making a landing page than then re-directs to the advertisers? Is it because their landing page is more of a 'pre-sell' page?

Why are you saying you can't direct link? Because the affiliate does not allow it or because - erroneously - you think the PPC network does not allow it? There's no rule in any PPC network I know of that prohibits direct linking, as long as that page follows all rules.

I gave the answer to your last question in my first post: you don't link to their sales page. When your visitors decide to buy, you can gather the information yourself and forward it to the affiliate as you suggested. Probably simpler, send them to the affiliate's page that does this data gathering which then takes them to the checkout.